PSOA2TPTP: A Reference Translator for Interoperating PSOA RuleML with TPTP Reasoners

Transcription

1 1 / 29 PSOA2TPTP: A Reference Translator for Interoperating PSOA RuleML with TPTP Reasoners Gen Zou 1 Reuben Peter-Paul 1 Harold Boley 1,2 Alexandre Riazanov 3 1 Faculty of Computer Science, University of New Brunswick, Fredericton, Canada 2 National Research Council Canada, Information and Communications Technologies 3 Department of Computer Science & Applied Statistics University of New Brunswick, Saint John, Canada

2 2 / 29 Outline

3 3 / 29 Outline

4 Interoperation Source PSOA RuleML Integrates relational and object-oriented modeling Generalizes RIF-BLD, F-logic and POSL Uses positional-slotted object-applicative (psoa) terms General case: o # f([t 1,1... t 1,n1 ]... [t m,1... t m,nm ] p 1->v 1... p k->v k) Special cases: o # f(t 1... t n p 1->v 1... p k->v k) o # f(t 1... t n) o # f( p 1->v 1... p k->v k) o # f 4 / 29

5 PSOA Example in Presentation Syntax (PS) 5 / 29 Document( Group ( Forall?Hu?Wi?Ch?o?1 (?o # _family(_child->?ch) :- And(?o # _family(_husb->?hu _wife->?wi)?1 # _kid(?wi?ch)) ) _f1 # _family(_husb->_joe _wife->_sue) _k1 # _kid(_sue _Pete) ) )

6 Interoperation Targets 6 / 29 TPTP s full First-Order Form (TPTP-FOF) Allows arbitrary first-order formulas Syntax and semantics Syntax Semantics Syntax Semantics ~p p v 1 = v 2 v 1 = v 2 p 1 & p 2 p 1 p 2 v 1!= v 2 ( v 1 = v 2 ) p 1 p 2 p 1 p 2?[v 1,..., v n ] : p v 1,..., v n : p p 1 => p 2 p 1 p 2![v 1,..., v n ] : p v 1,..., v n : p VampirePrime Open-source TPTP reasoner derived from the high-performance Vampire reasoner

7 7 / 29 Outline

8 Components and Workflow of PSOA2TPTP ANTLR: ANother Tool for Language Recognition ASO: Abstract Syntax Object 8 / 29

9 Workflow of ANTLR-Generated Components 9 / 29 AST: Abstract Syntax Tree (condensed tree encoding of the input stream)

10 10 / 29 Outline

11 11 / 29 Outline

12 12 / 29 Parser Grammar Rewriting ANTLR-generated parser uses LL (Left-to-right scanning, Leftmost derivation) mechanism The original EBNF grammar of PSOA/PS extended with syntactic sugar is non-ll and cannot be directly used as the ANTLR parser grammar We rewrite it into an LL(1) grammar, so that it not only can be accepted by ANTLR but is also more efficient Elimination of left recursion Left factoring

13 13 / 29 Parser Grammar Rewriting Elimination of left recursion example psoa : term '#' term ('(' tuples_and_slots ')')? term '(' tuples_and_slots ')' ; term : const var psoa external_term is rewritten to term : psoa non_psoa_term ; non_psoa_term : const var external_term ; psoa : non_psoa_term psoa_rest+ ;

14 14 / 29 Parser Grammar Rewriting Left factoring example tuples_and_slots: tuple* (term '->' term)* term+ (term '->' term)* ; is rewritten to tuples_and_slots: tuple+ (term '->' term)* term+ ('->' term (term '->' term)*)? ;

15 15 / 29 Outline

16 16 / 29 Normalization Static Tupribution and Slotribution Transform composite formulas into a conjunction of elementary constructs o # f([t 1,1... t 1,n1 ]... [t m,1... t m,nm ] p 1->v 1... p k->v k) = o # f() & o # Top(t 1,1... t 1,n1 ) &...& o # Top(t m,1... t m,nm ) & o # Top(p 1->v 1) &...& o # Top(p k->v k)

17 17 / 29 Translation of Elementary Constructs Terms Constants τ psoa (_C) = lc ( low line C) Variables τ psoa (?v) = Qv ( Question mark v) Tuple terms τ psoa (o # Top(t 1... t k )) = tupterm(τ psoa (o), τ psoa (t 1 )... τ psoa (t k )) Slot terms τ psoa (o # Top(p > v)) = sloterm(τ psoa (o), τ psoa (p), τ psoa (v)) Membership terms τ psoa (o # f()) = member(τ psoa (o), τ psoa (f))

18 18 / 29 Translation of Elementary Constructs Formulas Conjunction τ psoa (And(f 1... f n )) = (τ psoa (f 1 ) &... & τ psoa (f n )) Implication τ psoa (ϕ : ψ) = (τ psoa (ψ) => τ psoa (ϕ)) Existential Quantification τ psoa (Exists?v 1...?v n f) = (? [τ psoa (?v 1 )...τ psoa (?v n )] : τ psoa (f)) Universal Quantification τ psoa (Forall?v 1...?v n f) = (! [τ psoa (?v 1 )...τ psoa (?v n )] : τ psoa (f))

19 19 / 29 Translation of Queries Use reserved answer predicate ans to obtain the bindings for query variable?v i! [τ psoa(?v 1)...τ psoa(?v n)] : (τ psoa(q) => ans("?v 1 = ",τ psoa(?v 1),..., "?v n = ",τ psoa(?v n)))

20 20 / 29 Example Input Input knowledge base Document( Group ( Forall?Hu?Wi?Ch?o?1 (?o # _family(_child->?ch) :- And(?o # _family(_husb->?hu _wife->?wi)?1 # _kid(?wi?ch)) ) _f1 # _family(_husb->_joe _wife->_sue) _k1 # _kid(_sue _Pete) ) ) Query And(_f1 # _family(_husb->_joe _wife->_sue _child->?who) _k1 # _kid(_sue?who))

21 21 / 29 Example Normalization Normalized knowledge base Document( Group ( Forall?Hu?Wi?Ch?o?1 ( And(?o # _family()?o # Top(_child->?Ch)) :- And( And(?o # _family()?o # Top(_husb->?Hu)?o # Top(_wife->?Wi)) And(?1 # _kid()?1 # Top(?Wi?Ch))) ) _f1 # _family() _f1 # Top(_husb->_Joe) _f1 # Top(_wife->_Sue) _k1 # _kid() _k1 # Top(_Sue _Pete) ) )

22 22 / 29 Example Translation TPTP generated for knowledge base fof( ax01,axiom,(! [Q1,Qo,QCh,QWi,QHu] : ( ( member(qo,lfamily) & sloterm(qo,lwife,qwi) & sloterm(qo,lhusb,qhu) & member(q1,lkid) & tupterm(q1,qwi,qch) ) => ( member(qo,lfamily) & sloterm(qo,lchild,qch) ) ))). fof( ax02,axiom, ( member(f1,lfamily) & sloterm(f1,lwife,lsue) & sloterm(lf1,lhusb,ljoe) )). fof( ax03,axiom, ( member(lk1,lkid) & tupterm(k1,lsue,lpete) )).

23 23 / 29 Example Translation and Execution TPTP generated for query fof( query,theorem,(! [QWho] : ( ( member(f1,lfamily) & sloterm(f1,lwife,lsue) & sloterm(f1,lchild,qwho) & sloterm(f1,lhusb,ljoe) & member(lk1,lkid) & tupterm(lk1,lsue,qwho) ) => ans("?who = ",QWho) ) )). VampirePrime output Proof found «ans»("?who = ", lpete)...

24 24 / 29 Outline

25 25 / 29 PSOATransRun wraps PSOA2TPTP and VampirePrime into two REST services Translation: PSOA2TPTP Execution: VampirePrime Requests are sent via HTTP POST method Inputs and outputs are JSON-encoded strings Available online (documentation and system):

26 26 / 29 Outline

27 27 / 29 Summary We have implemented a first version of the PSOA2TPTP translator using the ANTLR v3 framework Thus provide a semantics-preserving translation from PSOA RuleML to TPTP PSOATransRun wraps PSOA2TPTP and VampirePrime into REST services for convenient access

28 28 / 29 Future Work Extend PSOA2TPTP capability to handle all PSOA RuleML constructs Implement the fully-aso-based translator Develop real-world Clinical Intelligence use case and others employing PSOATransRun

29 29 / 29 References Boley, H. A RIF-Style Semantics for RuleML-Integrated Positional-Slotted, Object-Applicative Rules In Bassiliades, N., Governatori, G., Paschke, A. (eds.) RuleML Europe, vol of LNCS, pp Springer, Zou, G., Peter-Paul, R., Boley, H. and Riazanov, A. PSOA2TPTP: A Reference Translator for Interoperating PSOA RuleML with TPTP Reasoners In: Bikakis, A., Giurca, A. (eds.) RuleML 2012, vol of LNCS, pp Springer, Al Manir, M.S., Riazanov, A., Boley, H. and Baker, C.J.O. PSOA RuleML API: A Tool for Processing Abstract and Concrete Syntaxes In: Bikakis, A., Giurca, A. (eds.) RuleML 2012, vol of LNCS, pp Springer, 2012.